Conclusion

 

A precise measurement of the pion beta decay rate will provide the opportunity for stringent tests of the current Standard Model, specifically testing the Conserved Vector Current hypothesis and constraining the Cabbibo Kobayashi Maskawa quark mixing matrix. The relatively simple transition of the pion beta decay, and the well understood radiative corrections, make this measurement a valuable and feasible task.

In the process of finishing construction of the PIBETA calorimeter, a measurement of the Panofsky Ratio has been made. This measurement is of interest because it connects the pion-nucleon scattering amplitude with the pion photoproduction amplitude, which facilitates the calculation of the former. By comparing information about the pion scattering amplitude derived from scattering data with that obtained from the measured value of the Panofsky Ratio, one can test the principle of isospin symmetry in the N system. The Panofsky Ratio value extracted from the 1997 measurement is 1.490.1, which agrees with the best measurement of 1.5460.009. [19]

This Panofsky Ratio measurement is of use to the PIBETA collaboration because it can be compared with the known result, thereby providing a test of the performance of the CsI calorimeter. In addition, the products of the Panofsky Ratio measurement include photons which are comparable in energy to those resulting from the pion beta decay reaction. Consequently, these photons have been used to determine the response of the PIBETA calorimeter in this energy range.

Because the Monte Carlo simulations of the experiments are crucial to the accurate extraction of the pion beta decay rate and the Panofsky Ratio, it is necessary to account for the light output and position-dependent nonuniformities of each CsI crystal in the calorimeter. These quantities have been measured using first cosmic muons and, most recently, 660 keV photons, and have been entered into the simulation as a smearing factor and a spatially dependent weighting function in the crystal energy depositions.

This spatially dependent weighting function has been shown to be most effective in the extraction of the Panofsky Ratio for events which are confined to the central six crystals of the forty-four element array. Because these six crystals were placed centrally for their exceptional light output uniformities, this would suggest that the Monte Carlo simulation has been more accurate in modeling the behavior of crystals with very uniform light reponses than otherwise. Consequently, it may be necessary to examine whether the tomography probe of 660 keV photons is sufficient to characterize the complete light reponse of the CsI crystals. However, a complete characterization may be unnecessary, because the final pion beta decay rate measurement involves photons and positrons with energies less than 70 MeV. These particles deposit their energy into regions of the CsI crystals which can be described adequately through tomography with the 660 keV photon probe.

Algorithms have been created for the absolute and relative energy calibration of the CsI crystals in the calorimeter. These algorithms have been shown to decrease the amount of noise in the data, as well as to improve the energy resolution of the calorimeter.

A shower reconstruction algorithm has been developed which locates the origin of the electromagnetic shower in the CsI and NaI arrays. Several parameters in the algorithm have been optimized to produce the best angular resolution. Geometric corrections have been applied based on the arrangement of the detectors. The resulting angular resolution is 1.8 and 1.2 for the CsI and NaI arrays, respectively.

A clustering algorithm has been tested which facilitates the study of optimal cluster size in the PIBETA calorimeter, for single particle final states in the 44-crystal array. The cluster size has been optimized with respect to energy resolution and event reconstruction efficiency. The optimal cluster size has been found to contain two rings of CsI crystals surrounding one central crystal.

Finally, with the calibrations and developments that have been presented here, a measurement of the pion beta decay should be feasible to within better than 0.5% accuracy.